# Finding Statistically Significant Interactions between Continuous Features

## TL;DR

This paper introduces a novel algorithm for efficiently identifying statistically significant interactions among continuous features, overcoming computational challenges and improving detection power in high-dimensional data.

## Contribution

It presents the first method to detect significant interactions among continuous features by deriving p-value bounds for effective pruning, enhancing computational efficiency and statistical power.

## Key findings

- Successfully detects all significant interactions in synthetic datasets
- Efficiently handles high-dimensional continuous feature interactions
- Outperforms existing methods in computational speed and accuracy

## Abstract

The search for higher-order feature interactions that are statistically significantly associated with a class variable is of high relevance in fields such as Genetics or Healthcare, but the combinatorial explosion of the candidate space makes this problem extremely challenging in terms of computational efficiency and proper correction for multiple testing. While recent progress has been made regarding this challenge for binary features, we here present the first solution for continuous features. We propose an algorithm which overcomes the combinatorial explosion of the search space of higher-order interactions by deriving a lower bound on the p-value for each interaction, which enables us to massively prune interactions that can never reach significance and to thereby gain more statistical power. In our experiments, our approach efficiently detects all significant interactions in a variety of synthetic and real-world datasets.